Combinatorial Problems and ExercisesBasic enumeration; The sieve; Permutations; Two classical enumeration problems in graph theory; Connectivity; Factors of graphs; Extremal problems for graphs; Spectra of graphs; Automorphism of graphs; Hypergraphs; Ramsey theory. |
Contents
Hypergraphs circuits transversal theory intersection | 521 |
Dictionary of the combinatorial phrases and concepts used | 528 |
Notation | 539 |
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1-factor 2-connected a₁ adjacent arises assertion assume automorphism b)-paths B₁ belongs bipartite circuit claim classes clearly color complete components connected Consider consists construction contains contradiction Conversely corresponding counted cover cycle defined degree denote Determine digraph directed disjoint distinct edges edges of G eigenvalues elements endpoints equal equivalent exactly exists faces fact fixed follows formula G₁ G₂ given graph G Hamiltonian hand Hence holds hypergraph implies independent induction joined k-coloration least length Let G matching Math maximum meet minimal Moreover neighbors Observe obtain obviously occur orientation otherwise P₁ pairs partition path permutation points problem Prove remove respectively resulting satisfies sequence side Similarly simple graph solution spanning subgraph subset Suppose theorem tree triangle trivial unique V₁ x₁ yields